Tryndamere is one of League of Legend's melee carry-s, which means, indeed, that he becomes nigh-unstoppable lategame as he gets more and more items (though despite what you may think, Tryndamere is not nearly as powerful now as he was back near release)
Tryndamere's counter is hard CC. If you don't have CC (which is quite possible in blind pick), you have no real option other than to prevent him from getting kills in the first place.
This is, in part, why Tryndamere is considered something of a "newbie stomper" - without CC and coordination, both often lacking in newer players, he can be a royal pain to deal with.
The truth of the matter is that Tryndamere, like all carry-s, is fragile. Without his ult, he melts like paper, especially under focus.
What Tryndamere wants you to do, more than anything else, is stand still and let him crit you to death. So don't let him - use your CC to snare him, slow him, keep him at arms length. (I dare say you'd be hard pressed to find a team of 5 without one slow or better betwixt all of them)
The goal when fighting Tryndamere should be to get him to use his ult, then disable him for its duration, then kill him. If he uses his ult to flee, all the better - re-engage on a team fight within 2 minutes, and it'll still be on cooldown, making him prime to focus.
In terms of surviving Tryndamere, you want armor, and lots of it. A Thornmail will cause Tryndamere's massive crits to likewise sliver his own health, while a Frozen Heart will reduce his attack speed while providing you armor (and mana).
The best option is to go premade with people you know.
If you solo then yes you should ask people what builds are they using and what lanes they want to be in,people will often be ok and tell you how they plan to play the game,but of course there are times when you just get people that want to troll and there is nothing you can do about it.
Personally what i sometimes do when i enter solo queue is that i type in:"STOP DON'T LOCK IN" as soon as i enter queue,and people often listen and do not lock it after that,and then i tell them that we should build our team carefully and most people are ok with that.
Of course some people get rude about it and lock in with random champion and there is nothing you can do about them,either dodge queue or stick with them and hope for the best.
I would also mention that even if you get really weird team combination that you can still win if you're lucky.Even if your team may have crappy combination there is a chance that enemy team doesn't have good combination either or that they don't know how to play their champions so good.So there is always hope.
Best Answer
ARAM champion selection is based only off of champions currently available to you. This includes all champions you own, plus all the ones that are available free at the time.